Christopher Columbus discovered previously unknown lands in 1492, and within twenty years the conquest of these new lands was proceeding quickly. The Spanish who came to settle the New World were generally not farmers and craftsmen but soldiers, adventurers and mercenaries looking for a quick fortune. Native communities were attacked and enslaved and any treasures they may have had such as gold, silver or pearls were taken. Teams of Spanish conquistadors devastated native communities on Caribbean islands such as Cuba and Hispaniola between 1494 and 1515 or so before moving on to the mainland.
The most famous conquests were those of the mighty Aztec and Inca Empires, in Central America and the Andes mountains respectively. The conquistadors who took these mighty Empires down (Hernan Cortes in Mexico and Francisco Pizarro in Peru) commanded relatively small forces: Cortes had around 600 men and Pizarro initially had about 160. These small forces were able to defeat much larger ones: at the Battle of Teocajas, Sebastian de Benalcazar had 200 Spanish and some 3,000 Cañari allies: together they fought Inca General Rumiñahui and a force of some 50,000 warriors to a draw.
How were the Spanish conquistadors able to do it? The Spanish armor and weapons had much to do with their success.
There were two sorts of Spanish conquistadors: horsemen or cavalry and foot soldiers or infantry. It was the cavalry that would usually carry the day in the battles of the conquest. Cavalrymen received a much higher share of the treasure than foot soldiers when the spoils were divided. Some Spanish soldiers would save up and purchase a horse as a sort of investment which would pay off on future conquests.
The Spanish horsemen generally had two sorts of weapons: lances and swords. Their lances were long wooden spears with iron or steel points on the ends, used to devastating effect on masses of native foot soldiers. In closer combat, a rider would use his sword. Steel Spanish swords of the conquest were about three feet long and relatively narrow, sharp on both sides. The Spanish city of Toledo was known as one of the best places in the world for making arms and armor and a fine Toledo sword was a valuable weapon indeed: the finely made weapons did not pass inspection until they could bend in a half-circle and survive a full-force impact with a metal helmet. The fine Spanish steel sword was such an advantage that for some time after the conquest, it was illegal for natives to have one.
Spanish footsoldiers could use a variety of weapons. Many people incorrectly think that it was firearms that doomed the New World natives, but that's not the case. Some Spanish soldiers used a harquebus, a sort of early musket. The harquebus was undeniably effective against any one opponent, but they are slow to load, heavy, and firing one is a complicated process involving the use of a wick which must be kept lit. The harquebuses were mostly effective for terrorizing native soldiers, who thought the Spanish could create thunder.
Like the harquebus, the crossbow was a European weapon designed to defeat armored knights and too bulky and cumbersome to be of much use in the conquest against the lightly armored, quick natives. Some soldiers used crossbows, but they're very slow to load, break or malfunction easily and their use was not terribly common.
Like the cavalry, Spanish foot soldiers made good use of swords. A heavily armored Spanish foot soldier could cut down dozens of native enemies in minutes with a fine Toledan blade.
Spanish armor, mostly made in Toldeo, was among the finest in the world. Encased from head to foot in a steel shell, Spanish conquistadors were all but invulnerable when facing native opponents.
In Europe, the armored knight had dominated the battlefield for centuries and weapons such as the harquebus and crossbow were specifically designed to pierce armor and defeat them. The natives had no such weapons and therefore killed very few armored Spanish in battle.